Solve (x^2)+(x^2+2)=410/6983(1-21)

$$( x ^ { 2 } ) + ( x ^ { 2 } + 2 ) = \frac { 410 } { 6983 ( 1 - 21 ) }$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{195335459}i}{13966}\approx -0-1.000733656i$$

$$x=\frac{\sqrt{195335459}i}{13966}\approx 1.000733656i$$

Steps by Finding Square Root

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+2=\frac{410}{6983\left(1-21\right)}$$

Subtract 21 from 1 to get -20.

$$2x^{2}+2=\frac{410}{6983\left(-20\right)}$$

Multiply 6983 and -20 to get -139660.

$$2x^{2}+2=\frac{410}{-139660}$$

Reduce the fraction \frac{410}{-139660} to lowest terms by extracting and canceling out 10.

$$2x^{2}+2=-\frac{41}{13966}$$

Subtract 2 from both sides.

$$2x^{2}=-\frac{41}{13966}-2$$

Subtract 2 from -\frac{41}{13966} to get -\frac{27973}{13966}.

$$2x^{2}=-\frac{27973}{13966}$$

Divide both sides by 2.

$$x^{2}=\frac{-\frac{27973}{13966}}{2}$$

Express \frac{-\frac{27973}{13966}}{2} as a single fraction.

$$x^{2}=\frac{-27973}{13966\times 2}$$

Multiply 13966 and 2 to get 27932.

$$x^{2}=\frac{-27973}{27932}$$

Fraction \frac{-27973}{27932} can be rewritten as -\frac{27973}{27932} by extracting the negative sign.

$$x^{2}=-\frac{27973}{27932}$$

The equation is now solved.

$$x=\frac{\sqrt{195335459}i}{13966} x=-\frac{\sqrt{195335459}i}{13966}$$

Steps Using the Quadratic Formula

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+2=\frac{410}{6983\left(1-21\right)}$$

Subtract 21 from 1 to get -20.

$$2x^{2}+2=\frac{410}{6983\left(-20\right)}$$

Multiply 6983 and -20 to get -139660.

$$2x^{2}+2=\frac{410}{-139660}$$

Reduce the fraction \frac{410}{-139660} to lowest terms by extracting and canceling out 10.

$$2x^{2}+2=-\frac{41}{13966}$$

Add \frac{41}{13966} to both sides.

$$2x^{2}+2+\frac{41}{13966}=0$$

Add 2 and \frac{41}{13966} to get \frac{27973}{13966}.

$$2x^{2}+\frac{27973}{13966}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and \frac{27973}{13966} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times \frac{27973}{13966}}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times \frac{27973}{13966}}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times \frac{27973}{13966}}}{2\times 2}$$

Multiply -8 times \frac{27973}{13966}.

$$x=\frac{0±\sqrt{-\frac{111892}{6983}}}{2\times 2}$$

Take the square root of -\frac{111892}{6983}.

$$x=\frac{0±\frac{2\sqrt{195335459}i}{6983}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±\frac{2\sqrt{195335459}i}{6983}}{4}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{195335459}i}{6983}}{4} when ± is plus.

$$x=\frac{\sqrt{195335459}i}{13966}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{195335459}i}{6983}}{4} when ± is minus.

$$x=-\frac{\sqrt{195335459}i}{13966}$$

The equation is now solved.

$$x=\frac{\sqrt{195335459}i}{13966} x=-\frac{\sqrt{195335459}i}{13966}$$